Inerton is a quasi-particle, i.e. an elementary excitation of the physical space, which carries a fragment of a local volumetric fractal deformation of the spatial tessel-lattice. The mathematical tessel-lattice consists of topological balls and represents the constitution of real physical space. Topological balls (which can be called superparticles) are primary entities of Nature and they densely fill the whole space, or the universe. In the tessel-lattice the size of an elementary cell can be compared with the Planck's fundamental length $l_{\rm f} =\sqrt{\hbar G/c^3} \sim 10^{-35}$ m. Under a local deformation of the tessel-lattice we understand a deformation of a cell. In physical language an inerton is an elementary excitation of space, which transfers a fragment of mass, because a local volumetric deformation of the mathematical tessel-lattice allows us to identify such spatial deformation with the physical notion of mass. An inerton migrates through the tessel-lattice by a relay mechanism carrying the state of local fractal volumetric deformation from cell to cell, which in some aspects similar to the hopping of an electron excitation from molecule to molecule in molecular crystals.

When a canonical particle moves through the cells of the tessel-lattice it interacts constantly with surrounding cells. As a result of such collisions spatial excitations must appear; they are referred to as inertons [1,2]. Inertia is associated with a kind of a resistance on the side of space at the motion of any object; hence, the inerton, as an elementary carrier of this field of inertia, is quite logical name for such an excitation of the tessel-lattice. The mass (i.e. local deformation of space) of a canonical particle is scattered due to the interaction with surrounding cells of space, such that around the particle a cloud of inertons is created which thus constantly accompanies the particle. It is interesting to note that this way of motion of a particle in the world ether was considered by Henri Poincaré far before the beginning of 20th century: a particle was treated as a singularity in the ether and moved through the ether surrounded by the ether's excitations [3]. Later, Louis de Broglie in his thesis of 1924 considered the motion of a particle that was guided by a real wave that spreads in a sub quantum space [4]; in our modern approach we can say that de Broglie treated the motion of a particle surrounded by the ether excitations as produced by the particle and these excitations were structured in a wave.

It has been shown [1,2] that a cloud of inertons appears around the particle moving in the real space and the inerton cloud has an expansion $\lambda/2$ (where the section $\lambda$ of the particle's path is identical to the de Broglie wavelength of the particle studied) and in transferal directions the inerton cloud covers the area $\pi \Lambda^2$ (where $\Lambda = \lambda c / \upsilon$ is the amplitude of the inerton cloud and $\upsilon$ and $c$ are velocities of the particle and light respectively).

The behaviour of inertons in the inerton cloud is as follows: The particle arriving at odd sections $\lambda/2$ of its path emits inertons that are scattered to the surroundings reaching the distance $\Lambda$ in transferal directions. The particle looses its velocity and stops. At the end of each odd section $\lambda/2$ the particle also nulls its mass.


Inertons, rejecting from the space at the distance $\Lambda$ from the particle, come back to it such that in each next even section $\lambda/2$ of the particle's path inertons return the velocity and mass to the particle. At the distance $\Lambda$ from the particle a local deformation of the kernel cell of the canonical particle, i.e. particle's mass m (Figure 1: a) is transformed to another type of distortion, namely a tension of the tessel-lattice $\xi$ (Figure 1: b); in other words, in this place the cell is not deformed volumetrically but shifted from its equilibrium position. It is this shift of cells in the tessel-lattice that generates the returning force in the elastic tessel-lattice, which replaces cells back into their original equilibrium positions. Coming back to the particle, inertons experience a gradual transformation from the tension to the local deformation: the tension decreases $\xi \rightarrow 0$ but the mass increases $0 \rightarrow m$. Thus from fragment to fragment inertons pass mass back to the particle (this is the subject of study of the theory of gravity) and return the velocity to the particle (this is the subject of study of submicroscopic mechanics).

If we only talk about the behaviour of the particle's mass we can say that the location of the mass periodically becomes point-like for a short moment until the inertons spread out again. But it is important to note that the whole cloud represents the particle.

The inerton cloud experiences oscillations of its density that is periodically transformed to the tension of space. This pattern is similar to the behaviour of photons, or the electromagnetic field in general, because during the motion of the photon a periodical transformation of its polarization from the pure electric to pure magnetic state takes place (and similarly the electric charge behaves as a motion too).

The velocity of motion of these bound inertons (i.e. the cloud's inertons) can be compared with the speed of light $c$. Harsh collisions, sharp stops and accelerations of a particle cause the ejection of free inertons from the inerton cloud. Under such conditions their velocity may exceed the speed of light up to two orders [5]. A free inerton migrates in the tessel-lattice similarly to an excitation migrating in a molecular crystal, i.e. the inerton hops from cell to cell through a relay mechanism. The path of an inerton can be subdivided by sections of the length $\lambda/2$. In odd sections $\lambda/2$ a local deformation (i.e. mass $\mu$ of the inerton) gradually drops to zero, but the tension $\xi$ increases (i.e. the size of each next cell increases to the size that exceeds that of a degenerate cell of the tessel-lattice). In even sections $\lambda/2$ the tension progressively decreases to zero but the mass $\mu$ is restored again.

So the motion of a free inerton features the wavelength $\lambda$ and is accompanied by the oscillation of its mass $\mu$ and the tension $\xi$ (compared with oscillations of parameters of the photon).


Figure 2: Motion of the free inerton along its path $\underline{ l }$; the volume of the appropriate cells changes, which means oscillation of the inerton's mass from $\underline{ \mu }$ in the point $\underline{ l=0}$ to zero in the point $\underline{l= \lambda/2}$ and so on.

Inertons carry not only mass; they are carriers also of fractal deformations of quantum systems because the tessel-lattice is endowed with certain fractal properties itself.

For the theoretical background of the concept of inertons see papers [1,2,6].

In conventional quantum mechanics, which is constructed in an abstract phase space, the inerton cloud manifests itself as the particle's wave $\psi$-function. Hence, an overlapping of wave $\psi$-functions of neutral particles (neutrons, atoms, etc.) is characterised by the exchange of inertons and that is why inertons become carriers of quantum mechanical forces (for instance, the so-called Casimir interaction, etc.).

Inertons are also carriers of gravity, i.e. the gravitational attraction between particles/objects, because they form a deformation field (i.e. a potential mass field) around bodies and due to the overlapping of these fields the exchange of inertons between the bodies has to occur instantly [7,8]. Inertons are also carriers of the so-called nuclear forces, which appear at short distances $\sim 10^{-15}$ m between nucleons [9].

So, there are only two basic fields of Nature: the inerton field and the photon field, which both are the consequence of the constitution of real space in the form of the tessel-lattice of primary topological balls (or superparticles).

The existence of inertons has been shown in many different experiments.


[1] V. Krasnoholovets and D. Ivanovsky, Motion of a particle and the vacuum, Physics Essays 6, no. 4, pp. 554-563 (1993) (also

[2] V. Krasnoholovets, Motion of a relativistic particle and the vacuum, Physics Essays 10, No. 3, pp. 407—416 (1997) (also:

[3] H. Poincaré, Sur la dynamique de l’électron, Comptes Rendus 140, pp. 1504-1560 (1905), Rendiconti del Circolo matematico di Palermo 21, 129-176 (1906); also: Oeuvres, t. IX, pp. 494-550 (and also in Russian translation: Selected Transactions, ed. N. N. Bogolubov (Nauka, Moscow, 1974), Vol. 3, pp. 429-486).

[4] L. de Broglie, Recherches sur la Théorie des quanta, Annales de Physique, 10e série, t. III (Janvier-Février 1925). (On the theory of quanta, translated by A. F. Kracklauer, 2004;; Morrisville, NC; 2007; ISBN: 978-1-84753-358-6)

[5] V. Krasnoholovets and J.-L. Tane, An extended interpretation of the thermodynamic theory, including an additional energy associated with a decrease in mass, International Journal of Simulation and Process Modelling 2, Nos. 1/2, pp. 67-79 (2006) (also (also

[6] M. Bounias and V. Krasnoholovets, Scanning the structure of ill-known spaces: Part 2. Principles of construction of physical space, Kybernetes: The International Journal of Systems and Cybernetics 32, No. 7/8, pp. 976—1004 (2003); (also

[7] V. Krasnoholovets, Gravitation as deduced from submicroscopic quantum mechanics, .

[8] V. Krasnoholovets, Reasons for the gravitational mass and the problem of quantum gravity, in Ether Spacetime and Cosmology, Vol. 1, Eds.: M. Duffy, J. Levy and V. Krasnoholovets (PD Publications, Liverpool, 2008), pp. 419-450 (ISBN 1873694105) (also

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